Onset of nonadiabatic particle motion in the near-Earth magnetotail

The onset of nonadiabatic proton motion is studied using direct integration of the Lorentz force equation of motion in the T89c magnetic field model with no electric field. Irreversible changes in the magnetic moment mu occur on traversals of the equator and give the gyrophase dependence predicted by Birmingham [1984]. Birmingham's expression delta(B) and the semiemipirical centrifugal impulse model of Delcourt et al. [1996] delta(CIM2) have linear regression coefficients with Delta mu/mu Of 0.99 and 0.95, respectively, for Delta mu/mu less than or equal to 1. By contrast, epsilon = 1/kappa(2) where kappa is the kappa parameter, has a linear regression coefficient with Delta mu/mu of only 0.5. To reliably estimate the onset of nonadiabatic behavior, one must therefore use delta(B) or delta(CIM2) rather than kappa. Using isocontours of constant delta(B) we map the regions of nonadiabatic ion motion. For a given energy the transition to nonadiabatic motion occurs over a radial distance of similar to 2 R-E On the nightside and is closest to the Earth at midnight. At midnight the nonadiabatic regime for protons extends inward to similar to 11 R-E (similar to 7.5 R-E) for 1 keV and to similar to 6 R-E (similar to 4.5 R-E) for 1 MeV with the Kp = 0 (Kp = 6) model. For O+ the nonadiabatic regime is 1.5 to 2 R-E closer to the Earth than for protons. Drift trajectory calculations and analytical estimates show that particles drifting through regions with delta(B) > 0.01 suffer net Delta mu similar to mu. The net Delta mu is extremely sensitive to initial gyrophase and it is shown that for delta(B) > 0.01 differences in gyrophase diverge exponentially with repeated equatorial crossings. Because the equatorial gyrophase determines the mu scattering, this implies that the mu scattering is chaotic so that no gyrophase-averaged invariant exists for the nonadiabatic drift motion. Despite this, the average, nonadiabatic drift paths are fairly well defined. The resulting hybrid drift consists of dayside adiabatic and nightside nonadiabatic drift. A single nonadiabatic nightside drift path is associated with a family of adiabatic dayside drift paths. If some of the adiabatic drift paths are open to the magnetopause, all of the particles on the family of hybrid drift trajectories will be subject to loss on a timescale comparable to the drift period. Because the nonadiabatic behavior is due solely to field line curvature, the same behavior will be present with a nonzero convection electric field with the important difference that the lower-energy particles will be on open convection drift paths. The hybrid drift path-induced loss effects are therefore most important for higher-energy particles, > 50 keV, whose adiabatic drift paths are closed in the presence of a convection electric field. The implications of nonadiabatic effects for ring current modeling based on Liouville's theorem apply equally well in the zero and finite electric field cases.